Formulation of theory of artificial earth satellite motion by Hori-Deprit method

A technique is proposed for eliminating both short and long period terms from the artificial earth satellite problem by use of a single canonical transformation. The proposed method for simultaneous exclusion of these terms can be used in combination with different variants of the averaging method. For example, if a semianalytical theory of motion of resonance satellites is formulated, the secular and resonance terms are retained in the Hamiltonian F(1) and the averaged system with this Hamiltonian is integrated numerically. The osculating elements are found from the mean elements using the formulas for replacement of variables derived in this article in which the generating function S characterizes aperiodic perturbations. The question of convergence of the presented algorithm remains open.